My 2.4 GHz cordless phone has several different frequencies. Every time you pick up the phone it starts up on a randomly selected one of the frequencies. There's a button to change to a different channel if there's interference. I also have a WiFi PC network running on 2.4 GHz. Frequently the phone will come up on the same channel as the PC netowrk - the phone works but the network drops right out for the duration of the call. I suspect your two phones will behave the same - OK most of the time but occasionally they will collide (but I think only if they're both in use).
You may want to consider one of newer 5.8 GHz cordless phones for a second unit. It won't interfere with your 2.4 GHz phone (nor your WiFi, for that matter).
[This message has been edited by pdhenry (edited 08-18-2003).]